A New Stochastic Duration Based on the Vasicek and Cir Term Structure Theories

Abstract

The stochastic duration based on the Vasicek and CIR models is theoretically superior to Macaulay's duration. However, empirical tests on bond immunization performance have so far failed to show its superiority. Within the one-factor framework, in this paper I propose to use a longer zero-curve yield instead of the original instantaneous interest rate as a proxy for the relevant risk source(s). I prove that the new duration becomes larger, increasing with bond maturity, than the original stochastic duration. Bond immunization using Belgian data shows that the new duration definitely beats the original stochastic duration and can in some cases outperform Macaulay's duration.

Keywords: Bond, One-Factor, Term Structure, Stochastic Duration, Immunization

JEL Classification: G10, G11, G13